The Cosmological Constant as a Gravitational Feedback Attractor: A Universality Theorem and Candidate Mechanism

We prove that within the class of cosmologies featuring negative feedback between Λ and gravitationally collapsed structure, the cosmological constant is a universal attractor whose location is mechanism-independent. The fixed point's existence follows from the intermediate value theorem; its uniqueness from monotonicity of the structure formation function. When the coupling amplitude falls within a broad range around the structure formation transition scale, the fixed point lies near the observed Λ ≈ 10⁻⁵² m⁻². The fixed point's sensitivity to the coupling constant is sub-linear — approximately 0. 20 for Press-Schechter structure formation, in the range 0. 09–0. 29 across mass-function variants — requiring the coupling to be specified only within roughly two orders of magnitude. Conditional on a mechanism that prevents bare vacuum energy from gravitating (Lombriser's backreaction or vacuum-energy sequestering approaches), the residual effective Λ is a convergence rather than a fine-tuning. This universality theorem unifies and explains several recent independent results: Lombriser's (2019) backreaction derivation of Ω_Λ = 0. 704, Farrah et al. 's (2023) observational evidence for BH-Λ coupling, and Bonanno & Reuter's (2002) self-adjusting RG fixed point. Each found the same Λ through different mechanisms because the fixed point is a topological feature of the feedback, not a consequence of any specific physics. The coincidence problem (why Λ ~ ρₘatter now) is simultaneously resolved: the fixed point is defined by their balance. We further propose the Connected Singularity Hypothesis (CSH) as one candidate mechanism, in which the future boundaries of all black hole interiors and the past boundary of the Big Bang are topologically identified as a single shared structure — replacing Smolin's per-black-hole offspring cosmology with a common convergence point. This cyclic framework is consistent with but not required by the universality theorem. We present an energy budget analysis, address known objections to cyclic cosmologies, and identify testable predictions including population-level statistical signatures in gravitational-wave echo phases, black hole mass-spin uniformity, and the LISA primordial gravitational-wave spectrum that would distinguish the CSH from other bounce cosmologies.